As an extension of our previous work[1]}, we adopted a 3D patch-based cGAN to generate a synthetic CT skull image given a T1-weighted MRI. Our 3D cGAN consisted of a generator \(G\)  and a discriminator \(D\) , where \(G\)  was trained to generate realistic CT skulls to fool the discriminator, while \(D\)  was trained to classify the real and synthetic CT skulls. For the generator \(G\) , we followed the network architecture in pix2pix[2]}, i.e., 2D ResNet[3]} with 9 residual blocks, and extended the network to 3D. The residual blocks were useful for shuttling the useful low-level features extracted from MR images, e.g., the location of prominent edges, directly to the deeper layers. At the output layer of \(G\) , we used Tanh as the activation function to map the logits to a bounded range of \([-1, 1]\) . As shown in DCGAN[4]}, this bounded output range allowed the model to learn more quickly to saturate during the training process. For the discriminator \(D\) , we adopted a 3D PatchGAN classifier[2]}, which could be run convolutionally to provide the ultimate output by averaging all responses across the whole volume.
